Question

Split into partial fractions
$\frac{1-x+2x^2}{{(1-x)}^3}$

Answer 1

To find the general term of the following expressions when expanded in ascending power of x .

$=\frac{1-x+2x^2}{(1-x{)}^3}$

Here , we have

$=\frac{1-x+2x^2}{(1-x{)}^3}$

The Expression can be written as

$=\frac{1-x}{(1-x{)}^3}+\frac{2x^2}{(1-x{)}^3}$

$=\frac{2}{(1-x{)}^3}-\frac{3}{(1-x{)}^2}+\frac{2}{(1-x)}$